Marsh was officially ruled out just 30 minutes before Wednesday night's toss after scans revealed he was suffering internal testicular bleeding from a blow he suffered at training earlier in the week.
Australia still managed to post a competitive 6-182 on the tricky wicket, with Marcus Stoinis (45 off 29 balls), Josh Inglis (37 off 17) and Matt Renshaw (37 off 33) all playing handy cameos.
In reply, Ireland slumped to 5-43 before their innings ended at 9-115 off 16.5 overs, with injured skipper Paul Stirling unable to return after aggravating a knee issue that first arose when he took a stunning catch earlier in the night.
Ellis (4-12 off 3.5 overs) tore through Ireland's top order before Zampa (4-23 off four overs) completed the demolition job.
Glenn Maxwell sent a scare through the Australian camp when he went off in the 12th over of Ireland's innings after stretching to save a boundary, but he was able to return a short time later.
The biggest question mark surrounds Marsh ahead of Friday's clash with Zimbabwe.
Such is the doubt surrounding Australia's T20 skipper, Steve Smith has flown to Sri Lanka as a stand-by player in case Marsh is unable to recover in time from his injury to play again in the tournament.
With Tim David (hamstring) also unavailable for selection for Wednesday night's match and Josh Hazlewood (Achilles tendon) already ruled out for the tournament, it meant Australia had only 12 fit players to choose from against Ireland.
After winning the toss and electing to bat, stand-in skipper Travis Head was given a life on six.
But his innings came to an abrupt end a few balls later during a disastrous mix-up with Josh Inglis, who had set off for a quick single from the non-striker's end despite his teammate's loud yell of "no".
Realising Inglis was already too far down the pitch, Head belatedly set off himself but was caught well short of his ground.
Cameron Green (21 off 11) was caught at mid-wicket, and Inglis was looking good until Stirling took a sharp jumping catch at cover as Australia slipped from 1-56 to 3-69.
Maxwell's departure heaped further pressure on Australia, but Stoinis and Renshaw helped stem the bleeding with a mature 61-run partnership that featured very few risks.
Ireland had a nightmare start to their run chase.
The luckless Stirling further aggravated his knee injury on the very first ball while setting off for a single, forcing him to retire hurt.
"It was pretty unfortunate to lose him like that," Stirling's teammate Lorcan Tucker said.
"He was brave and tried to go out and see the second innings off to a good start, but he wasn't able to unfortunately."
Although Renshaw was left red faced after dropping a sitter at point, Ireland slumped to 4-27 in the blink of an eye following a devastating burst from Ellis.
Ellis' first delivery was a thing of beauty - a slower ball from the back of his hand that totally bamboozled Ross Adair and crashed into his stumps.
The idea to start with a slower ball came after Ellis watched the lack of seam, swing and pace before he came on in the third over.
"I saw the swing king Xavier Bartlett start up, and there wasn't a lot of swing or seam there for him," Ellis said.
"So it sort of dictates what my overs in the back end of the power play and through the middle overs look like."
Curtis Campher was caught two balls later to hand Ellis his second wicket.
And Ellis had figures of 3-5 when Ben Calitz chopped him on.
Zampa joined in on the fun after that to ensure the cricket minnows were never truly in the hunt.
George Dockrell (41 off 29) top scored for Ireland, but he was stumped late in the innings off the bowling of Zampa.
